Question: 1. Given the following surfaces in cylindrical coordinates (a) z = 5r22rsin (b) rsec = 6 (c) z 4r2 +8rcos +6r2sin2 = 13 Find Cartesian

1. Given the following surfaces in cylindrical coordinates

(a) z = 5r22rsin

(b) rsec = 6 (c) z 4r2 +8rcos +6r2sin2 = 13 Find Cartesian equations and identify the surfaces.

2. Consider the parametric curve r(t) = t2,t 1,6 t2, t R.

(a) Find the points on the curve where the tangent line is parallel to the plane x+2y z = 3 (b) Show that the given curve is the intersection of a cylinder and a plane.

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